| Citation: | MIAO Jisong, SHAO Qiongling, REN Yuanet al. Coordinate rotation transformation method based on ternary angle[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2539-2546. doi: 10.13700/j.bh.1001-5965.2016.0882(in Chinese)
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Quaternion and Euler angle are used to describe coordinate transformation. Euler angle is characterized by three-time rotation and three parameters, and there are 12 kinds of rotation order. The characteristics of the quaternion are described by one rotation and four parameters. Using Euler angle is easy to cause gimbal lock phenomenon. Although it can avoid gimbal lock phenomenon, quaternion is more than Euler angles with one dimension and 33% amount of data. It may be illegal due to the accumulation of rounding error of floating point. To avoid the defects of the above methods, a new coordinate transformation method was proposed and two new concepts of deflection-vector axis and deflection-vector angle were introduced. The coordinate rotation transformation matrix based on the ternary angle was strictly deduced. Compared with the Euler rotation transformation, this method needs less rotation and avoids gimbal lock phenomenon; compared with the quaternion, it needs less parameters and is easy to understand. This method is more convenient for the description of the compound rotation. The proposed method provides more convenient mathematical means for the design and analysis of attitude transformation in related fields, such as inertial navigation and rotation modulation.
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